Journal of Integer Sequences, Vol. 23 (2020), Article 20.2.2

Stability for Take-Away Games

Simon Rubinstein-Salzedo
Euler Circle
Palo Alto, CA 94306

Sherry Sarkar
College of Computing
Georgia Institute of Technology
Atlanta, GA 30332


In this paper, we study a family of take-away games called α-TAG, parametrized by a real number α ≥ 1. We show that for any given α, there is a half-open interval Iα containing α such that the set of losing positions for α-TAG is the same as the set of losing positions for β-TAG if and only if β ∈ Iα. We then end with some results and conjectures on the nature of these intervals.

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(Concerned with sequences A002182 A004394 A040047 A323256 A323257.)

Received May 8 2019; revised versions received September 25 2019; October 2 2019. Published in Journal of Integer Sequences, January 1 2020.

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